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Aryne Reactions in the Synthesis of Heterocyclic Molecules
Get PDFReactive intermediates play an important the within the realm of chemical synthesis. Their high energy and transient nature make them difficult to observe and characterize, but it is these same properties that empower them to form bonds traditionally seen as difficult to prepare and unusual architectures quickly and efficiently. Herein, two reactive intermediates, arynes and transitient (2azaaryl)-cuprates, are exploited for their abilities to prepare important chemical motifs. Both serve as an avenue into the functionalization of arenes to provide products which hold value in a variety of fields including natural product total syntethis, pharmaseuticals and ligand design
Path-Integral and Coarse-Graining Strategies for Complex Molecular Phenomena
Get PDFMolecular simulation provides a powerful tool for connecting molecular-level processes to physical observables. However, the facility to make those connections relies upon the application and development of theoretical methods that permit appropriate descriptions of the systems or processes to be studied. In this thesis, we utilize molecular simulation to study and predict two phenomena with very different theoretical challenges, beginning with (1) lithium-ion transport behavior in polymers and following with (2) equilibrium isotope effects with relevance to position-specific and clumped isotope studies. In the case of ion transport in polymers, there is motivation to use molecular simulation to provide guidance in polymer electrolyte design, but the length and timescales relevant for ion diffusion in polymers preclude the use of direct molecular dynamics simulation to compute ion diffusivities in more than a handful of candidate systems. In the case of equilibrium isotope effects, the thermodynamic driving forces for isotopic fractionation are often fundamentally quantum mechanical in nature, and the high precision of experimental instruments demands correspondingly accurate theoretical approaches. Herein, we describe respectively coarse-graining and path-integral strategies to address outstanding questions in these two subject areas
Simulation of Premixed Hydrocarbon Flames at High Turbulence Intensities
Get PDFTurbulent premixed hydrocarbon flames in the thin and distributed reaction zones regimes are simulated using both Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES). A series of DNS is performed to study the transition from the thin reaction zones regime to the distributed reaction zones regime. Differential diffusion effects, distributed burning, and local extinctions are quantified. Different fuels, chemical mechanisms, and equivalence ratios are considered. The fuel Lewis number significantly influences the chemical source terms and turbulent flame speeds. More precisely, simulations with differential diffusion effects exhibit lower mean fuel consumption and heat release rates than their unity Lewis number counterparts. However, the differences are reduced as the reaction zone Karlovitz number is increased. The turbulent reaction zone surface areas increase with the turbulence intensity but aren't strongly affected by fuel, equivalence ratio, chemical mechanism, or differential diffusion. Unsurprisingly, changes in the integral length at a fixed Karlovitz number do not affect the chemical source terms but lead to an increase in flame surface area. Assumptions behind closure models for the filtered source term are then studied a priori using the DNS results. Using the concept of optimal estimators, it is shown that a tabulation approach using a progress variable and its variance can predict accurately the filtered progress variable source term. The filtered source terms are compared to predictions from two common presumed sub-filter Probability Density Functions (PDF) models. Both models show deviations from the filtered DNS source terms but predict accurately the mean turbulent flame speed. Finally, LES of experimentally-studied piloted premixed jet flames are performed using tabulated chemistry. Velocity and flame height measurements from simulations and experiments are compared. The LES are in good agreement with the experimental results for the four different hydrocarbon fuels and three different Reynolds numbers simulated. This corroborates that fuel and chemistry effects in turbulent flames are limited to effects present in laminar flames
Behavior of O(log n) Local Commuting Hamiltonians
Get PDFWe study the variant of the k-local hamiltonian problem which is a natural generalization of k-CSPs, in which the hamiltonian terms all commute. More specifically, we consider a hamiltonian H over n qubits, where H is a sum of k-local terms acting non-trivially on O(log n) qubits, and all the k-local terms commute, and show the following -
1. We show that a specific case of O(log n) local commuting hamiltonians over the hypercube is in NP using the Bravyi-Vyalyi Structure theorem.
2. We give a simple proof of a generalized area law for commuting hamiltonians (which seems to be a folklore result) in all dimensions, and deduce the case for O(log n) local commuting hamiltonians.
3. We show that traversing the ground space of O(log n) local commuting hamiltonians is QCMA complete.
The first two behaviours seem to indicate that deciding whether the ground space energy of O(log n)-local commuting hamiltonians is low or high might be in NP or possibly QCMA, though the last behaviour seems to indicate that it may indeed be the case that O(log n)-local commuting hamiltonians are QMA complete. </p
Numerical Investigation of Vertical-Axis Wind Turbines at Low Reynolds Number
Get PDFThis thesis is aimed at numerically investigating the aerodynamics and the starting of a vertical-axis wind turbine at low Reynolds number using the immersed boundary method. The influence of the Coriolis effect on dynamic stall is isolated by comparing the rotating airfoil to one undergoing an equivalent planar motion that is composed of surging and pitching motions that produce an equivalent speed and angle of attack variation over a cycle. At lower tip-speed ratios, the Coriolis force leads to the capture of a vortex pair which results in a significant decrease in lift when the angle of attack of a rotating airfoil begins to decrease in the upwind half cycle. In the absence of the wake-capturing, the equivalent planar motion is a good approximation to a rotating blade in a vertical-axis wind turbine.
Analysis on the starting torque shows that when the turbine solidity is lower than about 0.5, the starting torque distribution can be well-modeled by considering a single blade at different orientations, and starting torque distributions for multi-bladed turbines can be constructed by linearly combining the torques at the respective positions of the blades. Using this model, optimal configurations to start a multi-bladed low-solidity vertical-axis wind turbine is proposed.
A preliminary study is made to determine an optimal blade pitch for a single-bladed motor-driven turbine using optimal control theory. When the input power is minimized directly, the solution seems to converge to only a local minimum due to a lower input power reduction than that obtained by maximizing the mean tangential force. After a transient, both controls converge to time-invariant pitch angles of about the same magnitude but with opposite signs. The wake-capturing phenomenon observed in the uncontrolled case necessitates large input power. Under active control, the disappearance of wake-capturing and attendant changes in the flow field collectively result in a reduction of required input power.</p
Essays in Economic History and Applied Microeconomics
Get PDFThis thesis consists of three papers studying institutions that assess human capital and performance.
The first two chapters study the Chinese Civil Service Examination in 19th century Jiangnan. Chapter 1 investigates how much intergenerational mobility did the exam system actually induce. Results show that although nominally every male was allowed to participate, in any given generation, effective competition mostly took place among individuals with enough resources. Substantial advantages were enjoyed by families with established tradition of education investment and exam success. Multigenerational analysis reveals a much higher level of elite persistence than what could be captured in analyzing only two adjacent generations.
In Chapter 2, I track a sample of provincial graduates’ further progress in the national exams and their official career attainment about 20 years after they passed the provincial exam, with a focus on the role played by family background. I find that the competition in the national exam resembles a meritocratic competition when family background is measured only by the father's status. However, when family background is measured by the highest status achieved by immediate paternal ancestors going back three generations, the family background remains significant in predicting national exam success, after controlling for proxy measures of competence. On official career attainment, I find that provincial graduates whose fathers held higher offices were significantly more likely to obtain higher offices themselves. Fathers' office prominence were especially crucial for achieving positions beyond entry-level appointments. These results thus cast serious doubt on the thesis that the
imperial civil service was meritocratic. Considering the historical and institutional background, I suggest that nepotism and use of office purchase were likely to lie behind the importance of fathers' office holding to provincial graduates' career paths.
Chapter 3 is a joint work with Matt Shum and Xi Wu. We examine strategic behavior in "360-degree" performance appraisal systems, in which an employee is evaluated by her supervisor, subordinate(s), peers (colleagues) and himself/herself. Using proprietary data from a mid-sized Chinese accounting firm, we find that employees manipulate their ratings to peers: they grant better ratings to their less qualified peers while giving poorer ratings to their more qualified peers, compared with evaluations from employees who are not peers. In addition, this manipulation is mostly done by employees who themselves are less qualified. Altogether, this implies that more-qualified employees "lose" from the 360-degree evaluation scheme, and we show that their promotion chances would be (slightly) higher under the traditional "top-down" scheme in which their performance ratings is based only on the appraisal of their superiors. We discuss implications for improving a 360-degree performance appraisal
system.</p
Recovering Structured Signals in High Dimensions via Non-Smooth Convex Optimization: Precise Performance Analysis
Get PDFThe typical scenario that arises in modern large-scale inference problems is one where the ambient dimension of the unknown signal is very large (e.g., high-resolution images, recommendation systems), yet its desired properties lie in some low-dimensional structure such as, sparsity or low-rankness. In the past couple of decades, non-smooth convex optimization methods have emerged as a powerful tool to extract those structures, since they are often computationally efficient, and also they offer enough flexibility while simultaneously being amenable to performance analysis. Especially, since the advent of Compressed Sensing (CS) there has been significant progress towards this direction. One of the key ideas is that random linear measurements offer an efficient way to acquire structured signals. When the measurement matrix has entries iid from a wide class of distributions (including Gaussians), a series of recent works have established a complete and transparent theory that precisely captures the performance in the noiseless setting. In the more practical scenario of noisy measurements the performance analysis task becomes significantly more challenging and corresponding precise and unifying results have hitherto remained scarce. The available class of optimization methods, often referred to as regularized M-estimators, is now richer; additional factors (e.g., the noise distribution, the loss function, and the regularizer parameter) and several different measures of performance (e.g., squared-error, probability of support recovery) need to be taken into account.
This thesis develops a novel analytical framework that overcomes these challenges, and establishes {precise asymptotic performance guarantees for regularized M-estimators under Gaussian measurement matrices. In particular, the framework allows for a unifying analysis among different instances (such as the Generalized LASSO, and the LAD, to name a few) and accounts for a wide class of performance measures. Among others, we show results on the mean-squared-error of the Generalized-LASSO method and make insightful connections to the classical theory of ordinary least squares and to noiseless CS. Empirical evidence is presented that suggests the Gaussian assumption is not necessary. Beyond iid measurement matrices, motivated by practical considerations, we study certain classes of random matrices with orthogonal rows and establish their superior performance when compared to Gaussians.
A prominent application of this generic theory is on the analysis of the bit-error rate (BER) of the popular convex-relaxation of the Maximum Likelihood decoder for recovering BPSK signals in a massive Multiple Input Multiple Output setting. Our precise BER analysis allows comparison of these schemes to the unattainable Matched-filter bound, and further suggests means to provably boost their performance.
The last challenge is to evaluate the performance under non-linear measurements. For the Generalized LASSO, it is shown that this is (asymptotically) equivalent to the one under noisy linear measurements with appropriately scaled variance. This encompasses state-of-the art theoretical results of one-bit CS , and is also used to prove that the optimal quantizer of the measurements that minimizes the estimation error of the Generalized LASSO is the celebrated Lloyd-Max quantizer.
The framework is based on Gaussian process methods; in particular, on a new strong and tight version of a classical comparison inequality (due to Gordon, 1988) in the presence of additional convexity assumptions. We call this the Convex Gaussian Min-max Theorem (CGMT).</p
Molybdenum Quinonoid Complexes: Synthesis, Characterization, and Reactivity
Get PDFPi-bound Molybdenum-quinonoid complexes supported by pendant phosphines were prepared and investigated for metal-ligand cooperative reactivity and access to multiple equivalents of protons and electrons within a single transition metal complex. Chapters 3, 4, and 5 of this dissertation describe the synthesis, characterization, and reactivity of these complexes in the context of multiproton, multielectron chemistry and small molecule activation.
Chapter 2 presents the synthesis of an unprecedented bis-borane supported peroxide dianion, prepared from a mixture of ferrocenes, borane, and dioxygen. The peculiarity of such a structure is emphasized, and reactivity explored. While ferrocenes of varying reduction potential were found to lead to the peroxide, only tris(pentafluorophenyl)borane was found to yield isolable peroxide, with other boranes leading to oxygenation or borate formation.
Chapter 3 describes the synthesis of a series of π-bound Molybdenum-quinonoid complexes and explores their reactivity with dioxygen. The Mo-quinonoid interaction is probed and elucidated through a number of reactions and experiments, highlighting the importance of the electronic coupling of the metal center with the organic fragment on overall reactivity with O2.
Chapter 4 further explores the π-bound Molybdenum-quinonoid complexes in various protonation and oxidation states, totaling four electrons and two protons accessible to the system. Proton-coupled electron transfer was demonstrated in two different oxidation states, and the effects of the metal-quinonoid interaction on the transfer of protons and electrons investigated thermochemically.
Chapter 5 explores the potential for π-bound Molybdenum-quinonoid complexes to access inner-sphere reactivity. The activation of E–X bonds, including H2 and PhSiH3, is demonstrated, as well as catalytic hydrosilylation of aldehydes.
Appendix A describes initial investigations into the preparation of heterobimetallic complexes supported by the catechol-diphosphine ligand framework. The synthesis of heterobimetallic MoCu complexes is presented and their structural parameters discussed.
Appendix B outlines the synthesis of multinucleating ligand platforms based off bipyridine frameworks, for the preparation of biologically inspired multimetallic complexes. Dioxygen reactivity of a dicopper system is also briefly presented.
Appendix C contains relevant NMR spectra for the compounds presented in the preceding sections.</p
Structural and Biochemical Characterization of Ligand Bound States of the FeMo-Cofactor of Nitrogenase
Get PDFNitrogenase is the only known enzyme capable of nitrogen fixation, the reduction of dinitrogen to ammonia, a metabolically available form of nitrogen. Developing an understanding of the complex mechanism required for biological nitrogen fixation requires that the enzyme be characterized in catalytically relevant states, such as those involving ligand binding and reduction. Nitrogenase catalyzes this reaction through the cyclic interaction of two metalloproteins, the Fe-protein and the MoFe-protein which contain three distinct metalloclusters, in an ATP-hydrolysis dependent electron transfer reaction. The binding and subsequent reduction of substrates requires multiple electrons donated from the Fe-protein to the MoFe-protein, in which the active site is located. In this study, we have structurally characterized the binding of two inhibitors to the FeMo-cofactor, CO and the Se of SeCN-. Both interactions involve the displacement of a single S, and the Se was used as a label to follow the interchange of three S sites within the FeMo-cofactor during catalysis. These finding change any future approaches to characterize the mechanism of biological nitrogen fixation, requiring that structural changes be considered for substrate binding and reduction
Simulation Pipeline for Velocity Field Measurements using the Kinetic Sunyaev-Zel'dovich Effect
No full textThe kinetic Sunyaev-Zel 'dovich (kSZ) effect is of great cosmological interest for
providing precision measurements of peculiar velocity fields independent of systematics
present in other cosmological probes. The high precision kSZ measurements
on the horizon are expected to yield valuable constraints distinguishing between
competing cosmological models. Instrumental to kSZ astromony is the removal of
contaminating point sources, primarily radio and dusty, star-forming galaxies that
have bright emissions in kSZ spectral bands. As the precision of measurements
improve, the source removal residuals may become significant contributions to the
overall kSZ error budget. A full simulation is essential to characterizing these induced
errors. This study develops a procedure for contamination removal from first
principles, verifying its optimality against information theoretic limits. Models for
contaminating sources of increasing complexity are considered, at each step characterizing
the optimality of the subtraction compared to theoretical bounds. The final,
currently unfinished objective is to apply this subtraction procedure to a realistic
source distribution and understand the incurred systematics